Subset Synchronization of Transitive Automata
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10281308" target="_blank" >RIV/00216208:11320/14:10281308 - isvavai.cz</a>
Result on the web
<a href="http://eptcs.web.cse.unsw.edu.au/paper.cgi?AFL2014.26" target="_blank" >http://eptcs.web.cse.unsw.edu.au/paper.cgi?AFL2014.26</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4204/EPTCS.151.26" target="_blank" >10.4204/EPTCS.151.26</a>
Alternative languages
Result language
angličtina
Original language name
Subset Synchronization of Transitive Automata
Original language description
We consider the following generalized notion of synchronization: A word is called a reset word of a subset of states of a deterministic finite automaton if it maps all states of the set to a unique state. It is known that the minimum length of such wordsis superpolynomial in worst cases, namely in a series of substantially nontransitive automata. We present a series of transitive binary automata with a strongly exponential minimum length. This also constitutes a progress in the research of compositionsequences initiated by Arto Salomaa, because reset words of subsets are just a special case of composition sequences. Deciding about the existence of a reset word for given automaton and subset is known to be a PSPACE-complete problem, we prove that thisholds even if we restrict the problem to transitive binary automata.
Czech name
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Czech description
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Classification
Type
O - Miscellaneous
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-10799S" target="_blank" >GA14-10799S: Hybercubic, graph and hypergraph structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů